I don't know if there are any real rights or wrongs in these situations. If someone wants to be with you and work on a marriage they will, regardless of whether you do laundry or not.
Right now what you need to focus on is you and your child. The only factors you really have control or influence over. I know you don't want to hear this, but just work in your best self interests. Be smart. Talk to an attorney.
Don't project your beliefs onto him..."he is grieving, he is depressed, he has foo issues " that's just a waste of time. And usually ends up being our own false belief systems and not indicative in any way of what they are really thinking.
Take it day by day. Lots of self care. And give your little one lots of attention.
